Can anyone how to invite someone as a friend or join a group in this community?
If you go to someone's profile page, which you can get to by clicking the username, you can click the "request friendship" button. Assuming the other person accepts the friend request, they will be marked as a friend on your profile, and vise versa. From what I remember, it does not notify the other person that you sent them a friend request, so it may take awhile for people to notice they have pending friend requests.
As for groups on the forums, there is no built-in group support. However, since you can private message multiple people, I suppose you could create a group that way if you really wanted to.
You add friends by visiting their profile page and clicking on the "request friendship" button.